This paper reviews commonly used methods of analysing and interpreting nanoindentation test data, with a particular emphasis on the testing of thin films. The popularity of nanoindentation testing is evidenced by the large number of papers that report such measurements in recent years. Unfortunately, there appear to be several issues that are emerging as common sources of error in using this technique. The present paper is aimed at highlighting these errors for the benefit of those practitioners who wish to use the technique but are not fully conversant with the field.

Critical review of analysis and interpretation of nanoindentation test data

Refining a metal’s grain size can result in dramatic increases in strength, and the magnitude of this strengthening increment can be estimated using the Hall–Petch equation. Since the Hall–Petch equation was proposed, there have been many experimental studies supporting its applicability to pure metals, intermetallics and multi-phase alloys. In this article, we gather the grain-size strengthening data from the Hall–Petch studies on pure metals and use this aggregated data to calculate best estimates of these metals’ Hall–Petch parameters. We also use this aggregated data to re-evaluate the various models developed to physically support the Hall–Petch scaling.

/pdf/six-decades-of-the-hall-petch-effect-a-survey-of-grain-size-1nvd57tqv1.pdf

Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals

Publisher Summary This chapter presents the formalism and applications of cluster expansions to the problem of ab initio calculations of thermodynamic properties of crystalline alloys. The success of the method owes much to the parallel developments of statistical and quantum mechanical methods and, of course, to the availability of powerful computational hardware and software. The technique of orthogonal expansions in cluster functions has revolutionized the treatment of configurationally disordered systems. In addition to offering the most rational and general state-of-order description of alloys, cluster methods provide the rigorous and essential link between quantum and statistical mechanical aspects of first-principles thermodynamic calculations. Cluster functions constitute a complete orthonormal set. This basis set produces a rigorous cluster algebra that is used for systems containing an arbitrary degree of configurational order (or disorder). Cluster methods are, in principle, ideally suited for calculating alloy phase equilibria.

Cluster Approach to Order-Disorder Transformations in Alloys

All available literature on the constitution of Ti−Al is reviewed. Based on a critical evaluation of these data the phase diagram for this system is assessed.

Reassessment of the binary Aluminum-Titanium phase diagram

A study of the indentation size effect (ISE) in aluminum and alpha brass is presented. The study employs rate effects to examine the fundamental mechanisms responsible for the ISE. These rate effects are characterized in terms of the rate sensitivity of the hardness, ∂ H/ ∂ ln e eff , where H is the hardness and e eff is an effective strain rate in the plastic volume beneath the indenter. ∂ H/ ∂ ln e eff can be measured using indentation creep, load relaxation, or rate change experiments. The activation volume V ∗ , calculated based on ∂ H/ ∂ ln e eff which can traditionally be used to compare rate sensitivity data from a hardness test to conventional uniaxial testing, is calculated. Using materials with different stacking fault energy and specimens with different levels of work hardening, we demonstrate how increasing the dislocation density affects V ∗ ; these effects may be taken as a kinetic signature of dislocation strengthening mechanisms. We noticed both H and ∂ H/ ∂ ln e eff (V ∗ ) exhibit an ISE. The course of V ∗ vs. H as a result of the ISE is consistent with the course of testing specimens with different level of work hardening. This result was observed in both materials. This suggests that a dislocation mechanism is responsible for the ISE. When the results are fitted to a strain gradient plasticity model, the data at deep indents (microhardness and large nanoindentation) exhibit a straight-line behavior closely identical to literature data. However, for shallow indents (nanoindentation data), the slope of the line severely changes, decreasing by a factor of 10, resulting in a “bilinear behavior”.

Nanoindentation and the indentation size effect: Kinetics of deformation and strain gradient plasticity

A thermodynamic description of the Ti-Al system has been developed. Three different analytical descriptions were used to describe the three different types of phases occurring in the Ti-Al system: the stoichiometric compounds, the disordered solution phases, and the ordered inter-metallic compounds which have homogeneity ranges. A least-squares technique was used to optimize the thermodynamic quantities of the analytical description using experimental data available in the literature. The calculated phase diagram, as well as the thermodynamic func-tions, agree well with the critically evaluated experimental data from the literature.

Thermodynamic Assessment and Calculation of the Ti-Al System

A generalized approach is proposed to calculate the magnetic contribution to the thermodynamic functions of alloys. This approach is applied successfully to the Fe-Ni binary system. The predicted magnetic specific heat of the fcc phase at 75 at. Pct Ni is in agreement with the experimental data within the accuracies of the data and the predicted values. The magnetic contributions to the Gibbs energies of the fcc and bcc phases for the Fe-Ni alloys obtained from this approach are added to the nonmagnetic portion of the Gibbs energies. The nonmagnetic portion of the Gibbs energy of the fcc phase is obtained from extensive thermochemical data at high temperatures as discussed in the paper immediately following this one. The total Gibbs energies of the fcc, bcc, and the orderedγ′-(FeNi3) phases are then used to calculate/predict phase equilibria of the Fe-Ni binary at temperatures lower than 1200 K. The calculated equilibria are in agreement with available experimental data. In addition, a irascibility gap of the fcc phase at low temperatures is predicted, resulting in the formation of a monotectoid equilibrium at 662 K as given below: {fx1361-02} The existence of the miscibility gap is due to the magnetic Gibbs energy term of the fcc phase which is composition dependent. Experimental results reported in the literature support the predicted miscibility gap.

Magnetic contributions to the thermodynamic functions of alloys and the phase equilibria of Fe-Ni system below 1200 K

The relationship between the peak shape of a DTA curve and the shape of a phase diagram

The solid + liquid phase equilibria between α-Al and β-AlLi were determined using differential thermal analysis (DTA), metallography, and chemical analysis. Boron nitride (BN), which was found to be inert to these alloys, was used as the container. These measurements were carried out in order to resolve the discrepancies reported in the literature. The α-Al+β-AlLi eutectic temperature and composition were determined to be 600 °C±1 °C and 25.8±0.5 at. pct Li. Using these data and data reported in the literature concerning the phase equilibria and thermodynamic properties, thermodynamic models for all the phases were obtained by optimization. The thermodynamic values obtained for the β-AlLi phase describe not only the phase equilibria, but also yield structural defect data in agreement with measured values. The assessed enthalpies of formation, excess entropies of formation, and entropies of melting for all the intermetallic phases obtained are compared with empirical correlations when experimental data are not available. In addition to the stable diagram, a metastable diagram involving the δ′-Al3Li is also calculated from the thermodynamic models. The calculated diagram is in good agreement with the experimental data.

Phase equilibria of the Al-Li binary system

The current study was carried out with a view to investigating the influence of age-hardening parameters, aging temperature and time, on the tensile properties and quality indices of a high-strength Al-9 pct Si casting alloy, namely, 354-Al-9 pct Si-1.8 pct Cu-0.5 pct Mg. Quality charts were used as an evaluation tool for selecting the optimum conditions to be applied, in practice, in order to develop high strength and optimum quality in 354 casting alloy. Aging at a low temperature of 428 K (155 °C) was observed to produce the greatest strength and optimum quality in the 354-type castings compared to aging at higher temperatures. The peak strength observed for 354 alloy may be attained after shorter aging times on the condition that the aging temperature is increased. The aging times required for reaching peak strength in 354 alloys are 72 hours, 40 hours, 8 hours, 1 hour, and 15 minutes at aging temperatures of 428 K, 443 K, 468 K, 493 K, and 518 K (155 °C, 170 °C, 195 °C, 220 °C, and 245 °C), respectively. Aging treatment at higher temperatures is accompanied by a reduction in the tensile properties and quality index values of the castings; however, it also introduces the possibility of a significant economical strategy for minimizing the time and the cost of this same treatment. Aging treatment at a lower temperature of 428 K (155 °C) produces fine and dense precipitates displaying smaller interparticle spacing, while at higher aging temperatures, such as 518 K (245 °C), the precipitates are coarser in size, less dense, and more widely dispersed. The quality charts developed in the course of the current research facilitate the interpretation and evaluation of the tensile properties of the 354 alloy. Such charts provide a logical evaluation tool, from the metallurgical point of view, for an accurate prediction of the influence of aging parameters studied on the properties of the alloys. Depending on the required level of tensile properties and based on the quality charts developed, it is possible to make a rigorous selection as to the most suitable aging parameters to be applied to the 354 alloy so as to obtain the best possible cost-effective compromise between alloy strength and quality.

J. C. Lin

Papers

Thermodynamic Assessment and Calculation of the Ti-Al System

Magnetic contributions to the thermodynamic functions of alloys and the phase equilibria of Fe-Ni system below 1200 K

The relationship between the peak shape of a DTA curve and the shape of a phase diagram

Phase equilibria of the Al-Li binary system

Influence of Aging Parameters on the Tensile Properties and Quality Index of Al-9 Pct Si-1.8 Pct Cu-0.5 Pct Mg 354-Type Casting Alloys